how can I effectively compute expected value by histogram approximation of probability desnsity function

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Michal
Michal 2019-10-22
评论： the cyclist 2019-10-22
What is the proper way to compute effectively (fast) the expected value E(x) in a case when I have approximation of probability desity function f(x) by probability normalized histogram?
Is there (FEX) any code available?
  2 个评论
the cyclist
the cyclist 2019-10-22
In what form do you have the approximate pdf? Is it a MATLAB function? Or is it a series of discrete values at specific x locations? Or something else? Can you upload your input data?

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the cyclist
the cyclist 2019-10-22
There might be some nuances in the numerical integration, but here is the basic idea. You need to approximate the integral of x over the pdf.
% For reproducibility
rng default
% Simulated data -- normal centered on x=5.
N = 1000000;
x = 5 + randn(N,1);
% Get the probability density function. (You have these values already?)
[pdf_x,xi] = ksdensity(x);
% The bin width. (In this case, they are all equal, so I just take the first one.)
dx = xi(2) - xi(1);
% Calculate the total probability. (It should be 1.)
total_probability = sum(pdf_x*dx)
% Calculate the mean, which is the expected value of x.
mean_x = sum(xi.*pdf_x*dx)
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Michal
Michal 2019-10-22
OK ... thanks for basic info. I think the "nuances" of integration will be my main problem.
I will try to use matlab "discretize" function to find pdf approximation at my histogram points and then integration over x * pdf * width.

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